Set A has three elements and set B has four elements. The number of injections that can be defined from A to B is

Options

A. 144
B. 12
C. 24
D. 64

Explanation

To find the number of injective functions (or injections) from set A to set B, we can follow these steps:

### Step 1: Understand the concept of injective functions
An injective function (or one-to-one function) is a function where each element of set A maps to a unique element in set B. This means no two elements in set A can map to the same element in set B.

### Step 2: Identify the number of elements in each set
- Set A has 3 elements.
- Set B has 4 elements.

### Step 3: Calculate the number of choices for each element in set A
1. For the first element in set A, we have 4 choices in set B.
2. For the second element in set A, since one element from set B has already been used, we have 3 remaining choices.
3. For the third element in set A, since two elements from set B have already been used, we have 2 remaining choices.

### Step 4: Multiply the number of choices
The total number of injective functions can be calculated by multiplying the number of choices for each element:
\[ \text{Total injections} = 4 \times 3 \times 2 \]

### Step 5: Perform the multiplication
Calculating the above expression:
\[ 4 \times 3 = 12 \]
\[ 12 \times 2 = 24 \]

### Conclusion
The total number of injective functions from set A to set B is 24.

### Final Answer
The number of injections that can be defined from A to B is **24**.

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